Process control involves maintaining processes, such as industrial, commercial, or other processes operating on systems within desired operating limits. Such processes have variables that can be controlled, or set, to control and manipulate the process, other variables that can be measured to monitor the status of the process, and still other variables that cannot be controlled or that, for any of various reasons, are not controlled even though they could be. The problem of process control is to maintain a process within acceptable limits by controlling input variables of the process, using measurements of other variables as feedback to determine the status of the process.
Generally, a level 1 process control is the dynamic control of multiple process variables; a setpoint is a reference or target value to which a process controller (e.g., a level 1 process controller) attempts to maintain its process; and level 2 process control is the optimization of the level 1 process control setpoints. In some existing systems, a single gain matrix solution was adopted for the level 1 and level 2 controls in order to keep a multiple-input multiple-output (MIMO) process to known setpoints. Setpoints change with changes to the process. Setpoints also change with drift in the print engine. For example, in electrostatic printing systems, level 1 setpoints such as Vhigh and Vlow targets, change when the level 2 control system determines new level 1 setpoints to adjust for drift in developability. Also, some systems do not have a level 1 control loop. In such systems also, for the same setpoint target, the dynamic range of actuators, mechanisms that operate as part of a process, can change depending on the drift. Vhigh is the voltage to which the photoreceptor is charged before the exposure process is begun and Vlow is the voltage to which the photoreceptor charged area is discharged after being exposed to the laser beam. Actuators at each level of control action are the manipulated input variables used to control the process so that after all control actions are executed the process will be at a desired state. All the possible values (range of values) that an actuator can take to maintain a process in a desired state or to transform the process from one state to another state constitute the dynamic range of the actuator. For example, the charge on the photoconductor surface is maintained (or controlled) to a desired state by adjusting the voltage Vhigh. At the charging station, a corona generating device or other charging device generates a charge voltage to charge the photoconductive belt or drum to a relatively high, substantially uniform voltage potential. The corona generator comprises a corona generating electrode, a shield partially enclosing the electrode, and a grid disposed between the belt or drum and the unenclosed portion of the electrode. The electrode charges the photoconductive surface of the belt/drum via corona discharge. The voltage potential applied to the photoconductive surface of the belt or drum can be varied by controlling the voltage potential of the wire grid. Thus, the wire grid voltage, Vgrid, is an actuator. The actual voltage on the photoconductive surface, Vhigh, becomes the outcome of the control action initiated by the change in actuator values. Thus, when the system settles after a control action, the outcome of the control action will result with Vhigh reaching the desired state.
Electrostatic printing processes are one example of controlled processes. To achieve predictable print quality consistently time after time in electrostatic printing processes, important internal parameters, states of the system, are controlled by applying feedback to process actuators based on toner state measurements on the photoreceptor/intermediate belt or the drum. These loops maintain background, solid area development, and tone reproduction curves of individual primary colors by adjusting various internal process and image actuators operating at varying frequency while making prints. Because the dynamic range of actuators is limited to remain within practical limits, limits are set for charge voltage, exposure ROS intensity and the development bias voltage due to cost and other considerations. In existing systems, a multiple-input multiple-output (MIMO) single gain matrix solution is designed using state feedback (SF) methods. State feedback is a feedback control method that provides the ability to affect every state, which may be measured or estimated, through control actuation. The control actions (i.e., change in control input variables) are generated by summing the gain-weighted states through a gain matrix for a MIMO system and through a gain vector for a SISO (single-input single-output) system. This solution is used in some existing Xerographic systems. See L. K. Mestha, “Control Advances in Production Printing and Publishing Systems”, Published in the proceedings of IS&T's “The 20th International Congress on Digital Printing Technologies (NIP20)”, Oct. 31-Nov. 5, 2004, Salt Lake City, Utah; U.S. Pat. Nos. 5,749,021; and 5,754,918. As a result of this approach, the dynamic range of actuators required for control actions can become too large. That is, the control of the actuators can result in wide excursions sufficient to lead to many undesirable stability problems, particularly when systems, such as print engines, are operating at their limits. For example, in a level 1 process control loop, the actuators that are normally used for controlling the photoreceptor surface potential to within a precise range of Vhigh (the charge on the photoreceptor surface) and Vlow (the charge on the photoreceptor after it is discharged with a laser) are the grid voltage, Vgrid, and the exposure intensity, X, of the laser. The photoconductive surface is exposed at the exposure station when the modulated light (laser) beam impinges on the surface of photoreceptor, selectively illuminating the charged surface of photoreceptor to form an electrostatic latent image. The fully exposed portion of the photoreceptor depends on both the amount of exposure intensity of the laser and the grid voltage. The photoreceptor surface voltage, Vhigh, depends on the grid voltage. Thus, this type of system is called a two-input two-output control system with actuators Vgrid and X varying within the dynamic range of lower to upper bounds (or limits). Higher X can result in saturation of exposed photoreceptor, resulting in no change for Vlow. Similarly, always using higher Vgrid can reduce corotron life. Always operating at lower limit of Vgrid may not give sufficient developability. Hence, a robust MIMO control system should always use actuator values within their limits (near their “sweet spots”) and not have the need to be operated at their upper/lower limits. If actuators are operating at their limits, then the single gain matrix used in the control loop is requesting higher actuations than what would have been possible had the control system used multiple gain matrices. A second example is related to the fuel efficiency of a typical automobile. If the automobile always operates at its top speed (say >130 miles per hour assuming we are permitted to drive at that speed), the fuel efficiency can be very low because the “sweet spot” for best fuel efficiency is around 55-60 miles per hour. That is, for a nonlinear process control system, a single gain matrix solution is not optimal. Use of a single gain matrix can lead to large excursions of actuators and, in many instances, actuators operating at their limits. Thus, there is a need for methods and control systems that reduce large excursions.